The Carlyle Group and Welsh, Carson, Anderson & Stowe, the private equity firms, are thought to have made a profit of $1.9bn (€1.5bn) between them in less than two years on Dex Media, the US directories business.

The firms have realised nearly $3.5bn on their investment, understood to have been $1.6bn. This represents a multiple of 2.2 times their initial payment.